 5.3.1: 43 = ; 82>3 = ; 32 = . (pp. A7A8 and pp. A86A87)
 5.3.2: Solve: x2 + 3x = 4 (pp. A46A51)
 5.3.3: To graph y = 1x  223 , shift the graph of y = x3 to the left 2 units.
 5.3.4: Find the average rate of change of f1x2 = 3x  5 from x = 0 to x = ...
 5.3.5: The function f1x2 = 2x x  3 has y = 2 as a horizontal asymptote. (...
 5.3.6: A(n) is a function of the form f1x2 = Cax , where a 7 0, a 1, and C...
 5.3.7: For an exponential function f1x2 = Cax , f1x + 12 f1x2 = .
 5.3.8: The domain of the exponential function f1x2 = ax , where a 7 0 and ...
 5.3.9: The range of the exponential function f(x) = ax , where a 7 0 and a...
 5.3.10: The graph of the exponential function f1x2 = ax , where a 7 0 and a...
 5.3.11: The graph of every exponential function f1x2 = ax , where a 7 0 and...
 5.3.12: If the graph of the exponential function f1x2 = ax , where a 7 0 an...
 5.3.13: If 3x = 34, then x = .
 5.3.14: The graphs of y = 3x and y = a 1 3 b x are identical.
 5.3.15: In 1524, approximate each number using a calculator. Express your a...
 5.3.16: In 1524, approximate each number using a calculator. Express your a...
 5.3.17: In 1524, approximate each number using a calculator. Express your a...
 5.3.18: In 1524, approximate each number using a calculator. Express your a...
 5.3.19: In 1524, approximate each number using a calculator. Express your a...
 5.3.20: In 1524, approximate each number using a calculator. Express your a...
 5.3.21: In 1524, approximate each number using a calculator. Express your a...
 5.3.22: In 1524, approximate each number using a calculator. Express your a...
 5.3.23: In 1524, approximate each number using a calculator. Express your a...
 5.3.24: In 1524, approximate each number using a calculator. Express your a...
 5.3.25: In 2532, determine whether the given function is linear, exponentia...
 5.3.26: In 2532, determine whether the given function is linear, exponentia...
 5.3.27: In 2532, determine whether the given function is linear, exponentia...
 5.3.28: In 2532, determine whether the given function is linear, exponentia...
 5.3.29: In 2532, determine whether the given function is linear, exponentia...
 5.3.30: In 2532, determine whether the given function is linear, exponentia...
 5.3.31: In 2532, determine whether the given function is linear, exponentia...
 5.3.32: In 2532, determine whether the given function is linear, exponentia...
 5.3.33: In 33 40, the graph of an exponential function is given. Match each...
 5.3.34: In 33 40, the graph of an exponential function is given. Match each...
 5.3.35: In 33 40, the graph of an exponential function is given. Match each...
 5.3.36: In 33 40, the graph of an exponential function is given. Match each...
 5.3.37: In 33 40, the graph of an exponential function is given. Match each...
 5.3.38: In 33 40, the graph of an exponential function is given. Match each...
 5.3.39: In 33 40, the graph of an exponential function is given. Match each...
 5.3.40: In 33 40, the graph of an exponential function is given. Match each...
 5.3.41: In 4152, use transformations to graph each function. Determine the ...
 5.3.42: In 4152, use transformations to graph each function. Determine the ...
 5.3.43: In 4152, use transformations to graph each function. Determine the ...
 5.3.44: In 4152, use transformations to graph each function. Determine the ...
 5.3.45: In 4152, use transformations to graph each function. Determine the ...
 5.3.46: In 4152, use transformations to graph each function. Determine the ...
 5.3.47: In 4152, use transformations to graph each function. Determine the ...
 5.3.48: In 4152, use transformations to graph each function. Determine the ...
 5.3.49: In 4152, use transformations to graph each function. Determine the ...
 5.3.50: In 4152, use transformations to graph each function. Determine the ...
 5.3.51: In 4152, use transformations to graph each function. Determine the ...
 5.3.52: In 4152, use transformations to graph each function. Determine the ...
 5.3.53: In 53 60, begin with the graph of y = ex [Figure 31] and use transf...
 5.3.54: In 53 60, begin with the graph of y = ex [Figure 31] and use transf...
 5.3.55: In 53 60, begin with the graph of y = ex [Figure 31] and use transf...
 5.3.56: In 53 60, begin with the graph of y = ex [Figure 31] and use transf...
 5.3.57: In 53 60, begin with the graph of y = ex [Figure 31] and use transf...
 5.3.58: In 53 60, begin with the graph of y = ex [Figure 31] and use transf...
 5.3.59: In 53 60, begin with the graph of y = ex [Figure 31] and use transf...
 5.3.60: In 53 60, begin with the graph of y = ex [Figure 31] and use transf...
 5.3.61: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.62: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.63: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.64: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.65: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.66: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.67: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.68: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.69: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.70: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.71: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.72: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.73: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.74: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.75: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.76: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.77: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.78: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.79: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.80: In 61 80, solve each equation. Verify your results using a graphing...
 5.3.81: If 4x = 7, what does 42x equal?
 5.3.82: If 2x = 3, what does 4x equal?
 5.3.83: If 3x = 2, what does 32x equal?
 5.3.84: If 5x = 3, what does 53x equal?
 5.3.85: In 85 88, determine the exponential function whose graph is given.
 5.3.86: In 85 88, determine the exponential function whose graph is given.
 5.3.87: In 85 88, determine the exponential function whose graph is given.
 5.3.88: In 85 88, determine the exponential function whose graph is given.
 5.3.89: Find an exponential function with horizontal asymptote y = 2 whose ...
 5.3.90: Find an exponential function with horizontal asymptote y = 3 whose...
 5.3.91: Suppose that f1x2 = 2x. (a) What is f142? What point is on the grap...
 5.3.92: Suppose that f1x2 = 3x . (a) What is f142? What point is on the gra...
 5.3.93: Suppose that g1x2 = 4x + 2. (a) What is g1 12? What point is on th...
 5.3.94: Suppose that g1x2 = 5x  3. (a) What is g1 12? What point is on th...
 5.3.95: Suppose that H(x) = a 1 2 b x  4. (a) What is H1 62? What point i...
 5.3.96: Suppose that F1x2 = a 1 3 b x  3. (a) What is F1 52? What point i...
 5.3.97: In 97100, graph each function. Based on the graph, state the domain...
 5.3.98: In 97100, graph each function. Based on the graph, state the domain...
 5.3.99: In 97100, graph each function. Based on the graph, state the domain...
 5.3.100: In 97100, graph each function. Based on the graph, state the domain...
 5.3.101: If a single pane of glass obliterates 3% of the light passing throu...
 5.3.102: The atmospheric pressure p on a balloon or plane decreases with inc...
 5.3.103: The price p, in dollars, of a Honda Civic DX Sedan that is x years ...
 5.3.104: Exponential and Logarithmic Functions original area of the wound an...
 5.3.105: The function D1h2 = 5e0.4h can be used to find the number of milli...
 5.3.106: A model for the number N of people in a college community who have ...
 5.3.107: Between 12:00 pm and 1:00 pm, cars arrive at Citibanks drivethru a...
 5.3.108: Between 5:00 pm and 6:00 pm, cars arrive at Jiffy Lube at the rate ...
 5.3.109: Between 5:00 pm and 6:00 pm, cars arrive at McDonalds drivethru at...
 5.3.110: People enter a line for the Demon Roller Coaster at the rate of 4 p...
 5.3.111: The relative humidity is the ratio (expressed as a percent) of the ...
 5.3.112: Suppose that a student has 500 vocabulary words to learn. If the st...
 5.3.113: he equation governing the amount of current I (in amperes) after ti...
 5.3.114: If f is an exponential function of the form f1x2 = C # ax
 5.3.115: If f is an exponential function of the form f1x2 = C # ax
 5.3.116: Use a calculator to compute the values of 2 + 1 2! + 1 3! + g + 1 n...
 5.3.117: Use a calculator to compute the various values of the expression. C...
 5.3.118: f f1x2 = ax , show that f1x + h2  f1x2 h = ax # ah  1 h h 0
 5.3.119: If f1x2 = ax , show that f1A + B2 = f1A2 # f1B2.
 5.3.120: If f1x2 = ax , show that f1 x2 = 1 f1x2 .
 5.3.121: If f1x2 = ax , show that f1ax2 = 3f1x2 4a.
 5.3.122: The hyperbolic sine function, designated by sinh x, is defined as s...
 5.3.123: The hyperbolic cosine function, designated by cosh x, is defined as...
 5.3.124: Pierre de Fermat (16011665) conjectured that the function f1x2 = 21...
 5.3.125: The bacteria in a 4liter container double every minute. After 60 m...
 5.3.126: Explain in your own words what the number e is. Provide at least tw...
 5.3.127: Do you think that there is a power function that increases more rap...
 5.3.128: As the base a of an exponential function f1x2 = ax , where a 7 1 in...
 5.3.129: As the base a of an exponential function f1x2 = ax , where a 7 1 in...
Solutions for Chapter 5.3: Exponential Functions
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 5.3: Exponential Functions
Get Full SolutionsSince 129 problems in chapter 5.3: Exponential Functions have been answered, more than 36225 students have viewed full stepbystep solutions from this chapter. Chapter 5.3: Exponential Functions includes 129 full stepbystep solutions. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.